Paper prepared for the 10th Global Eonomi Analysis Conferene, "Assessing the Foundations of Global Eonomi Analysis", Purdue University, Indiana, USA, June 2007 Pries, Soial Aounts and Eonomi Models Sott MDonald University of Sheffield Abstrat Despite the fat that SAMs are widely used as the databases for CGE models there remains some onfusion over the relationship between the two; in partiular the impliations and meaning of the 'law of one prie appear to be poorly understood. This has two lear, and arguably, worrying impliations. First, a defiieny in understanding the aounting relationships in a SAM means that when ompiling a SAM it is likel that the strutural relationships in the eonomy may be misrepresented. And seond, any misunderstanding of the behavioural relationships in a CGE model, whih an be defined as theory with numbers, is highly likely to lead to flawed interpretations of the results from suh models. The disussion in this paper revisits the issues of the role of a prie system in soial aounts and then demonstrates how the resultant prie definitions require that all whole eonomy models that satisfy the onditions of being both omplete and onsistent MUST obey the 'law of one prie. The relevane of the 'law to the harateristis of ertain features of CGE models is demonstrated as is its relevane to the ompilation of SAMs. 1
1. Introdution Eonomists have been known to assert that aountants know the prie of everything and the value of nothing. While suh an observation may aurately reflet an attitude of many eonomists towards aountants it raises onerns about the degree of respet offered by eonomists towards the national aount statistiians who ompile the databases used in most applied eonomi models; espeially when those models are prie driven. More speifially it raises the spetre that eonomists do not understand the system of pries that underlies national aounts and are given their rihest speifiation in Soial Aounting Matries (SAM). 1 Sine it is now aepted that the databases for all empirial whole eonomy models are aounting systems (Stone, 1962) and that all suh databases an be represented as SAMs (Pyatt, 1987) 2 a lak of understanding of the prie system that underlies a SAM suggests the possibility of a serious inonsisteny between the work of national aount statistiians and eonomi modellers. Nowadays the potential benefits from representing data for whole eonomy models in the form of SAMs has been widely appreiated in the literature and is often a preferred option, e.g., Lofgren et al., (2001). This deision reflets some of the useful harateristis of SAMs; of these two features stand out. First, a SAM is a omplete and onsistent representation of (eonomi) transations within an eonomy 3 during a defined period of time: omplete in the sense that all transations are reorded and onsistent in the sense that every expenditure by an agent has a mathing and orresponding inome for another agent: onsequently the row and olumn totals are equal. And seond, a SAM is a parsimonious representation of the data that an highlight patterns of interdependene within an eonomy. Despite the fat that SAMs are widely used as the databases for CGE models there remains some onfusion over the relationship between the two; in partiular the impliations and meaning of the law of one prie appear to be poorly understood, e.g., the SAMs for CGE models with export transformation (CET) funtions 4 typially reord exports as a olumn of the same ommodity aounts as domesti (intermediate and final) demand, and some users have suggested that this demonstrates that the law of one prie does not hold. It 1 The prie system underlying the UN System of National Aounts (SNA) (UN, 1993) is the most widely used but arguments have been made for different systems, e.g., Pyatt (1991, 1994a and 1994b). 2 Stone (1962) demonstrated many years ago It is perhaps of interest to realise that the framework of any model onerned with the eonomy as a whole is always an aounting system. This is true whether we work with highly aggregated models suh as that underlying Keynes General Theory, the input-output model of Leontief or the still more ompliated variant with whih this series [A Programme for Growth] is onerned. (p v). Pyatt (1987) elaborated on this by demonstrating that Sine every eonomi model has its orresponding aounting framework, and sine every suh framework an be set out as a SAM, it follows that every eonomi model has a orresponding SAM. (p 330.] 3 An eonomy an be defined in numerous different ways to enompass anything from a household to the world via villages and nation states. 4 See for instane the models that follow the lead of Dervis et al., (1982). 2
is easily demonstrated that this represents a serious misunderstanding of both the aounting relationships in a SAM and the behavioural relationships of the CGE model. This has two lear, and arguably, worrying impliations. First, a defiieny in understanding the aounting relationships in a SAM means that when ompiling a SAM it is likely, with a high degree of probability, that the strutural relationships in the eonomy may be misrepresented. If suh a SAM is then used to alibrate a strutural, e.g., CGE, model the resultant analyses may well be flawed. And seond, any misunderstanding of the behavioural relationships in a CGE model, whih an be defined as theory with numbers, is highly likely to lead to flawed interpretations of the results from suh models. The disussion in this paper revisits the issue of the role of a prie system in soial aounts and then demonstrates, in setion 3, how the resultant prie definitions require that all whole eonomy models that satisfy the onditions of being both omplete and onsistent obey the law of one prie. The relevane of the law of one prie to the harateristis of ertain features of CGE models is demonstrated in setion 4. In the main this setion serves to illustrate that established, and widely used, models all follow the law of one prie. However, it also serves to demonstrate that all known CGE models, bar one, with multiple households render the seond law of welfare eonomis null and void; this is espeially worrying when CGE models are being used to analyse issues of inome distribution. Beause the role of the law of one prie is entral to general equilibrium models it is fundamental to the ompilation of SAMs, and in setion 5 it is shown that an understanding of the prie system underlying a SAM means that it is trivial to understand how a SAM an be extended to enompass aspets of eonomi relationships that may be regarded as important. This is illustrated by referene to disussions about the relationships between SAMs based on Supply and Use and Input- Output tables and the extension of a SAM to inlude home prodution for home onsumption. The disussion is however limited to ases where transations take plae within the SNA s prodution boundary. 5 These disussions, in setion 6, raise an interesting empirial issue; to what extent does a failure to understand the determination of the prie system underlying a SAM ompromise the results from CGE models. 6 An empirial example is developed to demonstrate the importane of (strutural) detail in eonomi models. The final setion, 7, offers some onluding omments; these inlude a all for eonomists to reengage with national aount statistiians so as to ensure the maintenane of an eonomially onsistent prie system within national aounts data, and to demonstrate greater respet for the produt of their labours. The paper starts with a desription of a SAM; this is based on the SAM that is used throughout the analyses. 5 A disussion of some of the problems assoiated with ompiling SAMs that inlude transations out with the SNA prodution boundary is provided by MDonald (2006). 6 This is arguably not an issue on a theoretial level sine the previous setions have shown that a misunderstanding of the prie system has non trivial theoretial impliations. 3
2. Soial Aounting Matries The development of national aounts and SAMs were both largely inspired by Sir Rihard Stone. 7 In essene a SAM is a ombination of the information ontained in aggregate national aounts data; the input-output shema devised by Leontief and disaggregated institutional (soial) data, in suh a manner as to ensure the full irular flow of an eonomy is aptured. An important dimension of a SAM is the emphasis upon the disaggregation of the institutional aounts, and hene it is ommon to find that SAMs ontain multiple representative household groups (RHG). The emphasis on the soial dimensions of eonomi systems is a distintive feature of SAMs, and is a partial explanation of why they have proved so popular to the study of developing eonomies where issues of welfare, poverty and inome distribution are onsidered most important. 2.1 What is a SAM? 8 A SAM is a system of single entry book keeping presented in the form of a square matrix wherein eah aount is represented by both a row and a olumn. The entries in the SAM are transation values, i.e., pries multiplied by quantities, with the row entries representing inomes to the respetive aounts and the olumns representing expenditures by the respetive aounts. Hene the entry in the i th row and j th olumn is simultaneously the expenditure by the j th aount on the produt of the i th aount AND the inome to the i th aount from sales of its produt to the j th aount. A SAM must be omplete and onsistent: omplete in the sense that it overs all transations in an eonomy and onsistent in the sense that eah expenditure by an agent has a mathing and orresponding inome for another agent. Hene, as onsequene of being omplete and onsistent, the total inome and the total expenditures for every aount must equate, i.e., p. q = T = T = p. q i = j ij ij ij ij ij ij i i j j where p ij and q ij are the prie and quantity of aount j used by aount i and T ij the transation (value) between aount j and i. A typial representation of a SAM is presented in Table 1. 9 A typial SAM onsists of 6 broad ategories of aounts: ommodities, ativities, fators, institutions (households, 7 Stone ontribution to eonomi and national aounts has been extensively reviewed. See Pesaran and Harourt (1991) for a review and omprehensive list of publiations. 8 The title of this setion is taken from King (1985), whih still provides one of the best introdutions to SAMs. 9 The representation used here differs from the standard format presented in the SNA (UN, 1993) by ollapsing the institutional aounts. This is a simplifiation that does not affet the subsequent argument but ensures that the representation is onsistent with the format typially used in SAMs to alibrate CGE models and thereby eases exposition. It is trivial to demonstrate that all the subsequent arguments in this paper would hold for a SAM with a SNA format. 4
inorporated business enterprises, government), apital (for investment and savings), and trade. Consider first the row aounts for ommodities; these identify the distribution of ommodities between intermediate and final demand where final demands are disaggregated aross different institutions and the apital aount. These are total demands for ommodities. In equilibrium the total demand for ommodities is equal to the total supply of ommodities, i.e., the row and olumn totals equate. By definition the total supply of ommodities inludes imports and duties paid on imports, i.e., imports are valued in domesti urreny units. The ommodity aounts therefore trae out the soures and destinations of ommodities in the eonomi system. Two points deserve highlighting; exports, and export taxes, are treated as part of the ommodity aount, and that export taxes are inluded as expenditures by the ommodity aount, and the SUPPLY matrix reords total domesti prodution of ommodities by ativities, with ativities able to produe multiple ommodities. 10 The olumn entries for ativity aounts reord the use of inputs by produtive ativities. These inlude intermediate inputs, both domesti and imported, and value added, whih is broken down so as to inlude payments to different fators, broadly or narrowly defined, expenditure taxes paid by ativities and input subsidies reeived by ativities 11. The olumn sums for the prodution aounts reord the total inputs to produtive ativities. In this example, as is ommon, the row entries only reord the output of ommodities by ativities. The ativity aounts therefore reord the produtive ativities of an eonomi system, i.e., the generation of value added. A major onern with the ativity aounts is therefore the payments to fators. The row entries for fator aounts are inomes to the labour and apital aounts for produtive servies; it is a ommon pratie to lassify all employers of fators in an eonomy as ativities, e.g., government and private employers of domesti employees. The sum of these plus any fator inomes from abroad are by definition GNP at fator ost. The expenditures by the fator aounts are reorded in the olumns. The fator inomes are distributed between different types of households as labour inome and distributed profits, and to firms as non-distributed profits. These distributions take plae after the payment of taxes et., to the government and payments to overseas owned fators. The institutional aounts inlude different household groups, enterprises, other institutional entities, e.g., non government organisations, and government. Inomes to institutions are reorded as row entries and expenditures as olumn entries. Note how the government is a reipient of 10 Some representations of the SUPPLY matrix of SAMs used to alibrate CGE models inlude only domesti prodution supplied to the domesti market; these only have entries on the prinipal diagonal and reord exports in the ativity aounts (see Dervis et al., 1982). This alternative is a redued form of the SAM represented in Table 1. 11 In the GTAP database input subsidies apture domesti support programmes. 5
multiple forms of inome: tax revenues, e.g., tariffs on imports, diret taxes, profit taxes et., distributed profits and transfers from abroad, e.g., aid. The Capital aount refers to investment and its funding. Commodities in the apital aount olumn reord investments whereas the funding of investment is reorded as savings by institutions and apital aount transfers from abroad. The rest of the world aount reords the trade aounts. This inludes urrent and apital aounts, and visible and invisible trade. Note that the rest of the world aount is important if the poliy issues being analysed are trade related. 6
Table 1 Struture of a SAM Expenditures 1 2 3 4 Inomes Fators Institutions Commodities Ativities Labour Capital Households Firms Governme 1 Commodities Intermediate inputs (Combined USE) 2 Ativities Domesti prodution (SUPPLY) 3 Fators Labour Wages Capital Profits & Rent Households onsumption Governme onsumpti 4 Institutions Households Labour inome Distributed profits Firms Nondistributed profits GovernmentTariffs; VAT; Export taxes, Sales taxes Prodution taxes National insurane Distributed profits; Taxes on profits Intrahousehold transfers Transfers Diret taxes Diret taxes 5 Capital Aount Household saving 6 Rest of World Imports (if) Fator payments Current transfers abroad 7 Total Total supply Prodution Fator outlay Households expenditures Transfer Transfer Firms saving Governme saving Firms expenditures Governme expenditu 7
2.2 Pries and Quantities in a SAM Sine a SAM reords transations eah entry is, by definition, the produt of a prie and a quantity. The SAM in Table 2 has 2 ommodity, 2 ativity, 2 fator, 2 household, 5 tax instruments, 1 government, 1 apital and 1 Rest of the World aounts for whih a (stylised) set of transations are expressed algebraially as pries and quantities. By definition the prie for any transation in a row is the same irrespetive of the agent/aount that makes the purhase. This means that the quantities in any row are measured in ommensurate units and hene they an be meaningfully summed so that the row totals are defined as the produt of the respetive prie and the sum of the quantities that are reorded in eah transation in the row; T = p q = p Q and q = Q ij i ij i i ij i j j by definition therefore the transations in eah row refer to items that are homogenous, i.e., undifferentiated, and do not differ by referene to the purhasing agent. 8
Table 2 Commodities Ativities Fators 1 2 a2 a3 f1 f1 h1 h2 t1 t2 t3 t4 t5 g k w 1 0 0 p q p q 0 0 p q p q 0 0 0 0 0 p q p q p q 1 1, a1 1 1, a2 1 1, h1 1 1, h2 1 1, g1 1 1, k1 1 1, w1 2 0 0 p q p q 0 0 p q p q 0 0 0 0 0 p q p q p q 2 2, a1 2 2, a2 2 2, h1 2 2, h2 2 2, g2 2 2, k2 2 2, w2 a1 pa1qa1, 1 pa1qa 1, 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2 p q p q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2 a2, 1 a2 a2, 2 f1 0 0 p q p q 0 0 0 0 0 0 0 0 0 0 0 0 f1 f1, a1 f1 f1, a2 f 2 0 0 p q p q 0 0 0 0 0 0 0 0 0 0 0 0 f 2 f 2, a1 f 2 f 2, a2 Households h1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Tariffs t1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Export Taxes t2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sales Taxes t3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Prodn Taxes t4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Diret Taxes t5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Government g 0 0 0 0 0 0 Capital k 0 0 0 0 0 0 0 0 0 0 0 Rest of World w 0 0 0 0 0 Totals Total 9
However, by definition the total inome to an aount, i.e., the row total, is idential to the total expenditure by that aount, i.e., the olumn total, and therefore the olumn total an also be defined as p i Q i, but while pq = pq j i ij i i is meaningful, beause the units (transation values) are ommensurate, i q ij = Q j is not meaningful beause the transation quantities are not ommensurate. Consequently the aounting identities require that the transation quantities in eah row are reorded in ommensurate units, i.e., the items are homogenous and hene should have, from an eonomi logi perspetive, a ommon single prie. 2.3 Different Pries in a SAM It is useful at this point to omment briefly of some of the definitions used for different pries in the SNA. In part this is to allow the subsequent use of speifi terms, and in part it is neessary to avoid onfusion, sine there are tendenies for alternative names to be used for these terms or for the teams to be misused. 2.3.1 Basi Pries Basi pries are defined in the SNA as the amount reeivable by the produer from the purhaser for a unit of a good or servie produed as output minus any tax payable, and plus any subsidy reeivable, on that unit as a onsequene of its prodution or sale. It exludes any transport harges invoied separately by the produer (UN, 1993, paragraph 205). Consequently transations in the supply matrix are valued in terms of basi pries, i.e., p a1 and p a2 are basi pries. 2.3.2 Produers Pries Produer pries are defined in the SNA as the amount reeivable by the produer from the purhaser for a unit of a good or servie produed as output minus any VAT, or similar dedutible tax, invoied to the purhaser. It exludes any transport harges invoied separately by the produer. (UN, 1993, paragraph 205) 2.3.3 Purhaser Pries Purhaser pries are defined in the SNA as the amount paid by the purhaser, exluding any dedutible VAT or similar dedutible tax, in order to take delivery of a unit of a good or servie at the time and plae required by the purhaser. The purhaser's prie of a good inludes any transport harges paid separately by the purhaser to take delivery at the required 10
time and plae (UN, 1993, paragraph 215). Consequently transations in the ommodity rows are defined in terms of purhaser pries, i.e., p 1 and p 2 are purhaser pries, whih are defined as basi pries plus any relevant ommodity taxes and trade and transport margins. These relationships are transparent and straightforward for a losed eonomy, sine there are no imports or exports or tariffs or export taxes; they are less obvious for an open eonomy. 3. Pries and Soial Aounts 12 The desription of a SAM in the previous setion was ouhed in terms of transations and asserted the law of one prie as definitional within the ontext of national aounts. However while this was a satisfatory aounting definition, that aords with eonomi logi, it was to some extent a onvenient abstration from an eonomi theoreti perspetive. The fundamental issue that was avoided was the eonomi rationale for the aounting definition; it seems to be have been forgotten that it was eonomi theoreti reasoning rather than aounting that underlay the development of the prie system. 13 The rationale derives not from some set of bookkeeping/aounting onventions but rather from a series of eonomi relationships; sine these are fundamental behavioural relationships that underpin a large proportion of modern eonomis they are entral to eonomi models alibrated from SAMs. 3.1 Prie Definitions and Aounting Identities Consider the entries in the primary ommodity row of the SAM in Table 2, although the same logi applies to all rows, and where the quantity units in the row are ommensurate. The row total is the total value of inome to the primary ommodity aount, or the total expenditure on that ommodity by agents in the eonomy, i.e., the total value of demand, and this is equal to the olumn total for the primary ommodity, i.e., the total value of supply. This satisfies the equilibrium ondition whereby total supply and total demand equate. Hene the prie, p(1), is the average revenue reeived for that ommodity. But this raises a question as to the interpretation of p(1) in the ontext of the olumn total; in this ontext p(1) is the average ost and therefore the aounting identity requires that average revenues are defined as idential to average osts, whih is onsistent, in eonomi theoreti terms, sine osts and pries are o determined. This applies to all rows and olumns and means that in all CGE models all pries are derived from aounting identities, whether or not the data are presented as a SAM sine the 12 The disussion in this setion derives largely from Pyatt (1987). 13 Among the major reasons for the development of national aounts was a desire to give empirial ontent to the Keynesian eonomi model. 11
databases for all (onsistent) CGE models an be represented as SAMs. Some examples will serve to illustrate how this works. 3.1.1 Domesti Prie of Imports Define the domesti prie of imports (PM ) as the world prie, if, of imports in domesti urreny units plus any import duties. The value of imports at domesti pries is therefore ( ) PM * QM = SAM (" row", ) + SAM " imptax", (1) where QM is the quantity of imports, whih is a simple aounting identity derived from the SAM. Expressing eah SAM transation as a prie multiplied by quantity, assuming import duties are defined ad valorem and simplifying produes ( ) ( * ) *1 ( )* PM * QM = pwm * ER * QM + pwm * ER * QM tm PM = pwm + tm ER where pwm is the world prie of imports in foreign urreny units, ER the exhange rate and tm the ad valorem import duty rate. Note how PM is average revenue that is determined by the ost omponents and therefore is the basi prie of imports. 3.1.2 Basi and Purhaser Pries of Composite Commodities A ommon speifiation in a CGE model is the use of the omposite ommodity onept whereby domestially produed and imported ommodities are aggregated. Hene the basi prie of the omposite ommodity (PQS ) an be speified, using (1) and (2), as ( ) ( ) ( ) ( ) ( ( PD * QD ) ( PM * QM ) PQS * QQ = SAM ( a, ) + SAM " imptax", + SAM " row", d = PD * QD + pwm * ER * QM + pwm * ER * QM * tm (3) = + whih an then be written as QD * QM PQS = PD + PM * QQ QQ (4) where QQ the quantity of the omposite ommodity, PD and QD the basi prie and quantity of the domestially produed ommodity. Hene the basi prie of the omposite ommodity is the weighted average of the basi pries of its omponents, i.e., osts. In this simple example, assuming a simple ad valorem (general) sales tax, purhaser pries (PQD ) are then defined as ( ( 1 ) ( ", ) ) PQD * QQ = PQS * QQ + SAM " saltax = PQS * QQ + PQS * QQ * ts (5) PQD = PQS + + ts ) (2) 12
where ts is the ad valorem sales tax rate, i.e., basi pries plus an ad valorem sales tax rate. In inlusion of trade and transport margins is a simple extension of the same logi. 14 3.1.3 Purhaser Prie of Commodities with VAT The existene of VAT adds an interesting ompliation. In an idealised situation all VAT on intermediate inputs is rebated and hene VAT is only levied on final demand ommodities. Therefore the prie paid varies by agent, whih requires different prie definitions for intermediate and final demand ommodities. Assume the row labeled saltax is in fat an ad valorem VAT, then there are two prie definitions for the purhaser pries of the omposite ommodity, i.e., where PQD a = PQS ( 1 ) PQD = PQS + + tv PQD i a and PQD i are respetively the intermediate and final demand purhaser pries and tv the ad valorem VAT rate. Note how the prie definitions preserve the eonomi logi of the law sine there is a unique prie formation for both purhaser pries even though the SAM representation suggests only a single prie; this ambiguity would of ourse be removed by segmenting the ommodity aounts between intermediate and final demand, in whih ase the SAM transation representing the VAT revenue by ommodity would have appeared in the olumn for the ommodity sold into final demand. The key point is learly NOT the SAM presentation but the knowledge that the saltax row in fat refers to a VAT that only applies to final demand, i.e., that the prie determination proesses were different. (6) 14 Defining an aount alled marg to arry the trade and transport transations osts, this an be written as where mm is the ad valorem margin rate. ( salta ) ( ) ( QQ * ) ( * * ) ( * ) + ( PQ * ) ( ) PQD * QQ = PQS * QQ + SAM " x", + SAM " marg ", = PQS * QQ + PQS * ts + PQS QQ mm = PQS + PQS ts S mm PQD = PQS *1+ ts + mm 13
Table 3 A SAM (extrat) for VAT System Expenditures 1a 1b 2 3 4 5 6 7 Inomes Fators Institutions Final Intermediate Ativities Labour Capital Households Firms Government Capital Rest of World Tota Commodities Commodities Aount 1a Final Commodities 0 0 0 0 0 Households onsumption 0 Government onsumption Investment Exports (fob) Tota dema 1b Intermediate Intermediate 0 0 0 0 0 0 0 Commodities inputs 2 Ativities Domesti prodution Domesti prodution 0 0 0 0 0 0 0 0 Produ 3 Fators Labour 4 Institutions Households Wages Fator Inomes from abroad Capital Profits & Rent Fator Inomes from abroad Firms GovernmentTariffs; VAT; Export taxes, Sales taxes 5 Capital Labour inome Distributed profits Nondistributed profits Prodution taxes National insurane Distributed profits; Taxes on profits Intrahousehold transfers Household Aount saving 6 Rest of World Imports (if) Fator payments Current transfers abroad 7 Total Total supply Prodution Fator outlay Households expenditures Transfers Transfers from abroad Transfers Transfers Transfers from abroad Diret taxes Diret taxes Transfers from abroad Firms saving Government saving Firms expenditures Government expenditures Total investment Capital transfers Foreign earnings GNP fator Househ inom Firm inom Govern t inom Tota savin Impor 14
3.2 Pries and Interdependene The relationship between average ost and average revenue also ontains another fundamental impliation for strutural whole eonomy models that are prie driven. Namely, interdependenies within the eonomi model are determined by the strutural information ontained within the olumns of the SAM sine it is these strutural relationships that determine the average osts and hene pries. Consequently it is the relative magnitudes of the entries in the olumns of a SAM, i.e., the supply side, that determine the struture of interdependenies and therefore have a fundamental influene upon model performane irrespetive of the speifi funtional forms used in a model. This has an important impliation for the ompilation of a SAM, and by analogy any data struture used for a CGE model; the relevant strutural information is ontained in the olumn entries i.e., the Leontief style 15 olumn oeffiients. Thus, when ompiling a SAM, it is imperative that an emphasis is plaed upon the preservation of the information ontent of EXPENDITURES by aounts. 16 4. The Law of One Prie and Computable General Equilibrium Models The relationship between osts and pries also provides the eonomi theoreti reason why the law of one prie holds in all onsistent CGE models. Eah set of ost strutures an only provide one prie; hene eah olumn of the SAM an only provide the information ontent for one prie and hene the prie for any row of SAM must be unique. Therefore all CGE models must adhere to the law of one prie ; if it is advoated that a model does not adhere to this law then either the advoate does not understand the model or the model is not onsistent, beause the law is simply a statement of the requirement that eah prie in the model is uniquely determined. If any prie is not uniquely determined there is the impliation that the model ontains redundant equations. While the universality of the law of one prie in CGE models is theoretially self evident it is nevertheless benefiial to demonstrate how it applies in the ontext of a number of features ommonly found in CGE models. 15 Derived using a normalised prie vetor. 16 This partially explains why using the RAS method to estimate a new SAM an produe suh unreliable results, sine the RAS method annot preserve the relative magnitudes of the olumn entries, see Lynh (1979). 15
4.1 The Armington Insight vv Homogenous Imports Consider first the ase of a CGE model that uses the onept of a omposite ommodity 17, e.g., models in the tradition of Dervis et al., (1984), and hene a model that is onsistent with the SAM data in Table 1. The onsumer prie (PQD ) is defined (see above) as ( 1 ) PQD = PQS + + ts (7) where PQS is the weighted average of the domesti supply (basi) prie (PD ) and the import prie (PM ), and the import prie is the world prie (pwm ), in domesti urreny units, times 1 plus the import duty rate (tm ). Hene an Armington funtion operates simply as a ost funtion over a speifi organisation of the entries in the ommodity olumns of the SAM, and therefore aords fully, and obviously, with the arguments for the law of one prie. 18 Now onsider a ase where there are separate ommodity aounts for the domestially produed ommodities and imports. 19 If the demand for ommodities by agents is expressed separately for imports and domestially produed ommodities then the law of one prie learly holds by definition. However it is pertinent to onfirm that the law of one prie holds if demand is expressed for omposite ommodities that are aggregates of differentiated imports and domestially produed ommodities, e.g., a ase where the arguments of household utility funtions are omposite ommodities. Sine this simply amounts to a series of Armington funtions that operate as ost funtions over paired sets of ommodities then this is no more than a generalised version of the omposite ommodity ase dealt with above: it therefore aords fully with the law of one prie. 4.2 Export Transformation Funtions vv Homogenous Exports Typially a SAM is presented with export transations (foreign demand for ommodities) appearing in the same (ommodity) rows as domesti demand, whih suggests that for the law of one prie to hold that the export prie should be the same as the domesti prie. This is the approah in Tables 1 to 3 above, but loser analyses of the behavioural relationships underpinning a model with export transformation (CET) funtions for exports, e.g., Dervis et al., (1984), demonstrates that this is potentially misleading, if parsimonious, SAM presentation of the data that obsures the behavioural assumptions. 17 In fat all known CGE models, as does most modern eonomis, make extensive use aggregator funtions that are in fat index number systems. On the relationships between aggregator (utility, prodution, Armington, et.,) funtions see Diewert (1976). 18 Note the maintained assumption that the sales tax is some form of general sales tax that applies equally to all agents. If the sales tax were some form of value added tax that was rebated - partially or wholly - to ativities that purhased the ommodities as intermediate inputs, but not final demand, the formulation is more omplex but the law of one prie still holds (see MDonald, 2007, for a model with a generalised treatment of VAT). 19 The GTAP model is an example of suh aa arrangement; see MDonald and Thierfelder(200?) for a SAM representation of the GTAP database. In fat the GTAP uses a generalisation of the omposite ommodity speifiation. 16
The use of an export transformation funtion involves the expliit assumption that eah ativity atually produes two variants of the single ommodity that are differentiated by destination - export and domesti ommodities. The standard behavioural assumption is that eah ativity produes a omposite ommodity (QXC ) using the single tehnology represented by the ativity speifi (omposite) prodution funtion, and then this omposite ommodity is differentiated aording to destination. An alternative interpretation of this behavioural model would be that the ativity had two tehnologies; one for the domesti ommodity and another for the export and that the omposite prodution funtion was some weighted average. 20 Suh a haraterisation of an eonomy ould be reorded as a SAM with two sets of ommodity and ativity aounts - one for the domesti ommodity and imports and the other for exports, see Table 4. For suh an eonomy the apparent anomaly of the breah of the law of one prie in the SAM disappears instantly. 20 This is onsistent with the fat that the funtional forms, i.e., aggregator funtions, used in CGE models are in fat index number systems. 17
Table 4 A SAM (extrat) for Exports from from Expenditures 1a 1b 2a 2 3 4 5 Inomes Fators Institutions Export Domesti Export Domesti Labour Capital Households Firms Government Capital Rest Commodities Commodities Ativities Ativities Aount 1a Export 0 0 0 0 0 0 0 0 0 0 Exp Commodities 1b Domesti 0 0 Intermediate Intermediate 0 0 Households 0 Government Investment Commodities inputs inputs onsumption onsumption 2a Export Export 0 0 0 0 0 0 0 0 0 Ativities prodution 2b Domesti Domesti 0 0 0 0 0 0 0 0 Ativities prodution 3 Fators 0 Labour 0 0 Wages Wages 0 0 0 0 0 0 Fato Capital 0 0 Profits & Rent Profits & Rent 0 0 0 0 0 0 Fato 4 Institutions 0 0 0 0 0 0 0 0 0 0 Households Labour inome Distributed profits 0 Transfers 0 Tran a Firms 0 Government Export taxes 0 0 0 0 Nondistributed profits Tariffs; VAT; Export taxes, Sales taxes Prodution taxes Prodution taxes National insurane Distributed profits; Taxes on profits Intrahousehold transfers 5 Capital Aount 0 0 0 0 0 0 Household saving 6 Rest of World 0 Imports (if) 0 0 Fator payments 0 0 Current transfers abroad 7 Total Export supply Domesti Supply Export Prodution Domesti Prodution Fator outlay Transfers Transfers 0 Tran a Diret taxes Diret taxes 0 0 Tran a Households expenditures Firms saving Government saving 0 Firms expenditures Government expenditures 0 C tr 0 Total investment F ea 18
19
The prie definitions from the SAM in Table 4 are straightforward. For the export ommodity ( ) SAM e," row" = SAM ( ae, e) + SAM (" exptax", e) ( ) ( *1 ( ) PE * QE = PD * QE + PE * QE * te (8) e e e e e e e PE = PD + te e e e and the definition for the domesti ommodity is an obvious permutation of the previously derived definition. To omplete the argument it is ritial to onsider the pries used to value the supply matrix in Table 1. The orret prie is the basi prie, whih in the above analyses is PXC. This is simply a share weighted average of the export (PE ) and domesti (PD ) pries, i.e., a prie index. However this does raise a non obvious issue assoiated with the hoie of an export transformation funtion; namely the input ost shares for the export and the domesti ommodity are required to be idential if there is only one ativity aount that produes omposite ommodities that are aggregates of domesti and export ommodities. This sidesteps the requirement for two ativity aounts by allowing the use of a single (omposite) prodution funtion for both the domesti and export ommodities, but involves the hidden presumption that although the ommodities are differentiated the prodution funtions are idential. Hene there is a tension in any CGE model that inludes a CET formulation for the modelling the assumption that the domesti and export ommodities are differentiated. Namely despite the presumption of differentiation the ommodities are produed with idential tehnologies AND the input mix of the relevant ativities does NOT hange as the output mix hanges. Finally it is interesting to assess the differene between a model that assumes the export and domesti ommodities are differentiated and one in whih they are homogenous. The only differene is that the requirement for two different ativity aounts is no longer neessary. Sine the export and domesti ommodities are homogenous they are pried identially (PE PXC PD ) it is only neessary to reord two types of ommodity aount - one for the domesti ommodity and imports and the other for exports. The separate export aount is required beause of the possibility of export and sales taxes means that the export and (omposite) domesti purhaser pries might differ despite a ommon basi prie. Thus whether it is assumed that the domesti and export ommodity are homogenous or differentiated does not alter the implied requirement for two sets of ommodity aounts; one for the domesti ommodity and another for exports. ) 20
4.3 Sales Taxes and the GTAP Model A SAM representation of the GTAP database (MDonald and Thierfelder, 2004) at first sight seems to suggest that the law of one prie holds in the ase of the GTAP model. But loser inspetion indiates that the entries in the domesti ommodity rows are valued at basi pries, whih begs the question of the derivation of purhaser pries in the model and hene of onsisteny with the law of one prie. 21 The data in the SAM indiate that purhaser pries for domestially produed are defined as basi pries plus sales taxes 22 but that the ad valorem sales tax rates are purhasing agent AND ommodity speifi, i.e., the proportionate markup on basi pries for the same ommodity differs by purhasing agent. Thus it appears that the GTAP model does not onform to the law of one prie. In fat the GTAP model onforms fully with the law. In the GTAP model the effetive purhaser prie of any domesti ommodity is defined as where g = ( + g, ) g PDD, PXC *1 ts sa sa g PDD, sa produed ommodity, ommodity and is the GTAP purhaser prie for purhasing agent sa of the domestially g ts, sa g PXC is the GTAP basi prie of the domestially produed is the domestially produed ommodity and purhasing agent, sa, speifi ommodity tax. Sine the GTAP model assumes export and domestially produed g g g and sold ommodities are homogeneous, i.e., PXC PE PD. Exatly the same logi applies to the treatment of imports and onsequently the law of one prie holds for all ommodities and agents in the GTAP model. Notie how there is a symmetry in the GTAP model between the treatment of exports and domestially produed ommodities sold on the domesti market; the distintion by agents is in effet implemented on the supply side of the model, whih ensures onformity with the law of one prie as being the supply determination of pries. The obfusation of the operation of the law of one prie arises from the peuliar format adopted for the SAM representation of the GTAP database, not from the behavioural relationships in the GTAP model. In order to redue vastly the number of rows and olumns in the SAM the ommodity rows were valued at basi and NOT, as is arguably appropriate, purhaser pries. Suh a representation is onsistent with the GTAP onvention of using (symmetri) input-output tables as the data format for inter industry and final demand transations (see below for a disussion of input-output vv supply and use formats in SAMs). In the same manner the disaggregation the total indiret taxes on ommodities paid by agents is onsistent and neessary for meaningfully reording the data. However the information (9) 21 The reording of exports in the domesti ommodity rows has been dealt with above. 22 Note how the SAM indiates that the purhasing agent makes two payments when purhasing a ommodity; one to the produer at basi pries and another to the government via the paired sales tax aount. 21
requirements for suh a representation are enormous, whih begs the question about data reliability. 23 4.4 The Seond Law of Welfare Eonomis General equilibrium eonomis are intimately related to welfare eonomis, 24 and a ommon use a CGE models, following Adelman and Robinson (197?), has been to assess the inome distribution and welfare impliations of eonomi poliy hoies - espeially for developing ountries. However all bar one known CGE model formulates the funtional distribution of inome in suh a manner that NO seond law of welfare eonomis effets an arise. An understanding of the operation of the law of one pries makes the reason for this transparent. The onern here is with the behavioural relationships that relate to the household by fator sub matrix of SAM. 25 A typial behavioural assumption, e.g., Lofgren et al., (2001), 26 is that fixed value shares of fator inomes are distributed to eah household. This appears to be an eminently sensible behavioural assumption that is, under ertain irumstanes, fully onsistent with the law of one prie. But under the ommon fator market learing assumption that a fator is not fully employed and a perfetly elasti supply is available at the prevailing (real) market fator prie, it is arguably flawed. At first it is not immediately obvious what the orret pries are for the rows in the household by fator sub matrix. However this matrix reords the inome to households with respet to the fators they own, the servies from whih are sold to the fator aounts at, assuming the fators are homogenous, a ommon prie. If the unemployed fator is sold at a ommon prie then the value shares are idential to the fator (servie) quantity shares. Consequently the assumption of onstant value shares means that the quantity shares are assumed to remain onstant whih requires that any hanges in the quantity of that fator employed is drawn from eah household in the same ratio as provided in the situation prevailing in the base period of the SAM. Therefore the underlying behavioural assumption is that the distribution of fator ownership is onstant and hene there is no sope for hanges in the volumes of employment to generate redistributive effets in line with the seond law of welfare eonomis. 23 Version 6 of the GTAP database ontains approximately 600,000 potentially different sales tax rates. 24 Note how it is almost standard pratie to use summary welfare measures when analysing results from CGE models. 25 This argument ould be applied to the sub matries relating to the inome to ALL domesti and foreign institutions from the domesti fator aount, but exposition is eased by onentrating on household inomes only. 26 In fat the same applies to the GTAP model but the existene of one (regional) household renders issues of the seond law of welfare eonomis irrelevant 22
5. Developing Soial Aounting Matries for Eonomi Models It was argued at the start of this paper that not only did all whole eonomy models onform to the law of one prie but that understanding the law was important for the onstrution of databases to alibrate suh models. The previous analyses have onentrated on the appliation of the law to CGE models; this setion uses two examples to demonstrate the importane of understanding the law for ompiling databases/sams for suh models. The first example relates to the seemingly innouous issue of the appropriate format for reording inter industry and final demand data, while the seond deals with the seemingly diffiult, but in fat (theoretially) simple, issue of reording home prodution for home onsumption. 5.1 Input-Output vv Supply and Use Tables Until now a maintained assumption in the SAM has been that eah ativity produes a single ommodity and eah single ommodity is produed by only one ativity. 27 The advantage of this maintained assumption has been that the issue of input-output versus supply and use format is avoided; the SAM had simultaneously both an input-output and supply and use format. However, input-output tables are almost invariably, and always so if derived in aordane with the SNA (UN, 1993), redued forms derived from supply and use tables (see Miller and Blair (1985), Armstrong (1975), UN (1999)). The standard approah is to value the SUPPLY table and input-output tables at basi pries and the USE table at purhaser pries, and to generate symmetri input-output tables, valued at basi pries, by using the information in the supply and use tables. In pratie to derive suh input-output tables it is neessary to develop domesti and import use matries; revalue the use matries in basi pries; deide whether to use ommodity or ativity aounts for the inter industry rows and olumns of the input-output tables 28 ; and determine the tehnology assumptions that will be used to identify the prodution tehniques used for seondary produts. 29 The literature on these proesses is now old and the mehanis are well doumented and the harateristis of input-output tables are well known, even if they are not well understood by some users of the tables. It is the impliations of these proesses for eonomi models, rather than the proesses themselves that are of interest here. 27 This was relaxed when onsidering the ase of the Armington insight and export transformation funtions. 28 That is deide whether to form ommodity by ommodity or industry by industry tables. 29 There is a wide range of suh tehnology assumptions; these range from pure ommodity to pure industry assumptions via a spetrum of hybrid and by-produt tehnology assumptions (see Miller and Blair (1985) for an introdution. 23
The key argument is that any apparent advantages from an input-output format are very unlikely to be ahieved beause of the restritive nature of the assumptions required for the linear transformation of the data and the diffiulties generated for additional data olletion. 5.1.1. Choie of ommodity or industry aounts and Additional Data The hoie of ommodities or ativities as the basis for the row and olumn aounts of the input-output tables means that the other set of row and olumn entries must be adjusted to ensure that row and olumn total equate, e.g., if the ativity aounts provide the row and olumn totals the entries in the ommodity rows and olumns must be adjusted and hene no longer represent natural ommodities. This means that ANY other data must be redefined to maintain definitional onsisteny, e.g., if the household onsumption aount is to be disaggregated this is best done BEFORE generating the input-output tables so that the appropriate adjustments an be applied to all RHGs. The same basi argument applies if the ommodity aounts provide the row and olumn totals; the ativity aounts no longer represent natural ativities. Consequently full onsisteny in data definitions requires that a disaggregated SAM is developed on the basis of a SUPPLY and USE format PRIOR to onverting the SAM to an input-output format. 5.1.2 Tehnology assumptions and Modelling Prodution The appliation of ANY tehnology assumption to generate symmetri input-output tables imposes a linear transformation of the data in the SAM so as to remove seondary prodution, i.e., non prinipal ommodity prodution, from the SAM. While this ahieves a simplifiation of the modelling of prodution relationships it does so at the expense of sidestepping potentially important issues in the prodution proess. For instane agriulture is an industry overwhelmingly haraterised by multi produt firms; the seletion of an input-output format expliitly ignores this feature of the industry. In some instanes this may not be seem to be an issue, e.g., in the GTAP model where distributional issues are not pertinent due to the use of a single RHG, but this ignores issues about the ability of the agriultural industry to adjust its output struture - this issue is addressed in the OECD s GTAP-EM model. In other ases, e.g., where regional differenes in agriultural produt struture are an issue (PROVIDE, 2006), or where home prodution for home onsumption is a fundamental harateristi of an eonomy (MDonald, et al., 2007), deisions on produt output mix may be of ritial importane AND it may be appropriate to have ertain fators fixed. 30 30 Lofgren et al., (2001) is an example of one treatment of multi produt firms, but this adopts what is effetively a byprodut tehnology assumption whereby the output mix is fixed. An alternative approah, wherein industries an hange produt output mix in response to hanges in relative pries is used in MDonald and Punt (2007). 24
5.1.3 Information requirements The transformation of a supply and use SAM to an input-output format is very data intensive, and moreover the additional data are typially those least readily available. Imports The need for both domesti and import USE matries is a major data requirement. National aount statistiians may regard the data underpinning an aggregate use matrix as reasonably reliable, beause they are typially based upon surveys that ask about ommodity use by agents, but rarely ask how muh was imported and how muh was domestially produed - if only beause purhasers are unlikely to know the answer. Consequently where domesti and imports use matries exist they are usually less reliable than an aggregated use matrix. So not only is the proess of devising symmetri input-output tables data intensive it is also likely to involve the use of less reliable data. 31 But, even if ompletely reliable use matrix data are available it is still appropriate to first devise the SAM in a SUPPLY and USE format; at that point it is still questionable what benefits are ahieved by onverting to an input-output format. Tax revenues and/or rates 32 Information on taxes is without question among the most important data for ompiling a SAM and any subsequent model. Hene by definition more information is better, provided the data quality does not deline to rapidly. However tax data are not as readily available or reliable as might be wished, and/or governments are relutant to be expliit about tax revenues. Thus it is not unommon to find that SUPPLY tables only report the total tax revenue for eah ommodity, i.e., all ommodity taxes (import duties, export taxes, sales taxes, VAT, exise taxes, et.,) are lumped together as a single vetor. Even where the transations for different tax instruments are expliitly quantified, this is typially done as series of vetors rather than as matries that are tax instrument and purhasing agent speifi. Consequently if inputoutput tables in basi pries are developed and matries of tax revenues for eah tax instrument are produed from vetors of tax instrument speifi revenues the tax rates for eah instrument will be invariant aross ALL agents. This is an evitable onsequene of an embedded assumption of the law of one prie in the data organisation and manipulation 31 Still less appealing is the adoption of a naive assumption; namely that the import/domesti mix in eah transation is in the same proportions as the aggregate import to domesti supply mix for that ommodity. The information ontent of suh an assumption is virtually idential to that ahieved in a SAM with omposite ommodity aounts. 32 For a SAM the standard requirement is to ollet tax revenue data sine the interest is in transation values, i.e., realised rates rather than published rates. All too often however the gaps between realised and published rates are substantial, whih auses some problems. In addition eonomists sometimes wish to use rates that are equivalent to the effet of multiple interventions, e.g., tariff equivalents, but this raises diffiult issues relating to the identifiation of the rents assoiated with non tariff barriers. 25